Add Binary - Practice Coding Problems

Add Binary - Problem

Given two binary strings a and b, return their sum as a binary string.

A binary string contains only characters '0' and '1'. You need to perform binary addition following the same rules as decimal addition, but in base 2.

Binary Addition Rules:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (0 with carry 1)

Input & Output

Example 1 — Basic Addition

$ Input: a = "11", b = "1"

› Output: "100"

💡 Note: Binary addition: 11₂ + 1₂ = 100₂ (which is 3 + 1 = 4 in decimal)

Example 2 — Different Lengths

$ Input: a = "1010", b = "1011"

› Output: "10101"

💡 Note: Binary addition: 1010₂ + 1011₂ = 10101₂ (which is 10 + 11 = 21 in decimal)

Example 3 — Single Digit

$ Input: a = "1", b = "1"

› Output: "10"

💡 Note: Binary addition: 1₂ + 1₂ = 10₂ (which is 1 + 1 = 2 in decimal)

Constraints

1 ≤ a.length, b.length ≤ 10⁴
a and b consist only of '0' or '1' characters
Each string does not contain leading zeros except for the zero itself

Visualization

Tap to expand

Understanding the Visualization

Input

Two binary strings: "1011" and "1"

Process

Add bit by bit from right to left with carry

Output

Result binary string: "1100"

Key Takeaway

🎯 Key Insight: Binary addition follows the same carry logic as decimal, but carries occur when sum ≥ 2

Asked in

f Facebook 15 G Google 12 a Amazon 8

The key insight is to simulate manual binary addition from right to left with carry propagation. The optimal approach uses bit-by-bit addition, handling different string lengths gracefully. Time: O(max(n,m)), Space: O(max(n,m))

Common Approaches

Approach	Time	Space	Notes
✓ Convert to Decimal	O(n)	O(1)	Convert both binary strings to decimal, add them, convert back to binary
Bit-by-Bit Addition with Carry	O(max(n,m))	O(max(n,m))	Simulate manual binary addition from right to left, tracking carry

Convert to Decimal — Algorithm Steps

Convert binary string a to decimal integer
Convert binary string b to decimal integer
Add the two decimal numbers
Convert sum back to binary string

Visualization

Tap to expand

Step-by-Step Walkthrough

Convert to Decimal

Parse binary strings as base-2 numbers

Add Decimals

Perform regular decimal addition

Convert to Binary

Transform result back to binary string

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

char* solution(char* a, char* b) {
    // Convert binary strings to decimal
    unsigned long numA = strtoul(a, NULL, 2);
    unsigned long numB = strtoul(b, NULL, 2);
    
    // Add them
    unsigned long result = numA + numB;
    
    // Convert back to binary
    char* binary = malloc(65 * sizeof(char));
    if (result == 0) {
        strcpy(binary, "0");
        return binary;
    }
    
    char temp[65];
    int i = 0;
    while (result > 0) {
        temp[i++] = '0' + (result % 2);
        result /= 2;
    }
    
    // Reverse the string
    for (int j = 0; j < i; j++) {
        binary[j] = temp[i - 1 - j];
    }
    binary[i] = '\0';
    
    return binary;
}

int main() {
    char a[10001], b[10001];
    fgets(a, sizeof(a), stdin);
    a[strcspn(a, "\n")] = 0;
    fgets(b, sizeof(b), stdin);
    b[strcspn(b, "\n")] = 0;
    
    char* result = solution(a, b);
    printf("%s\n", result);
    free(result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Converting strings to integers and back takes O(n) time

✓ Linear Growth

Space Complexity

O(1)

Only storing integer values, not counting output string

✓ Linear Space

89.5K Views

Medium Frequency

~15 min Avg. Time

2.8K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Convert to Decimal — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler